Transcript Palo Alto Slides

Optimizing Electricity
Procurement for the
City of Palo Alto
IEOR 180 Senior Project
Toni Geralde
Mona Gohil
Nicolas Gomez
Lily Surya
Patrick Tam
Outline
• City of Palo Alto
• Energy deregulation
• Tradeoffs
• Palo Alto’s current decision making
tools
• Our linear optimization model
• Results
Company Background
Founded: 1900
Area: 26 square miles
Customers: 58,100 including
• residential homes
• small businesses
• corporate offices
• manufacturing facilities
• excluding Stanford University Campus
California Energy
Deregulation
• Began January 1, 1998
• Open buyer and seller
market for electricity
– Purchase Energy $X per Mega
Watt Hour
California Energy
Market
Inflexible products: Flexible products:
constant amount/
fixed prices
variable amounts
Forwards
Spot market
High Load
Load Load
All Week
WAPA
Trade-Offs
• Futures contracts:
– safeguard against price spikes versus
cost of premium
• Spot Market
– flexibility of amount versus exposure to
risk
Meeting Demand
Spot
Market/WAPA
Product
III
MWh
pri
Sell to spot
Product II
Demand Curve
Product I
12am
Time of Day
11:59 pm
Palo Alto Model:
Challenges
• How much WAPA should be utilized
– capacity charge based on maximum amount
• How much to purchase in advance via
forwards
City of Palo Alto:
Current Solution
• Optimize portfolio with two time periods:
– Heavy load hours (HLH)
– Light load hours (LLH)
• Purchase options: Forward contracts and WAPA
MW
LLH
HLH
LLH
Demand curve
6 am
Time of day
10 pm
Problem Statement
• Optimize available energy sources
with additional energy products and
additional time periods to
accommodate them:
–
–
–
–
–
WAPA
HLH forwards
LLH forwards
E3 blocks
All week forwards
Approach:
Linear Program
• Based in Excel and What’s Best Solver
E3 II
L
o
a
d
E3 I
WAPA
6am
10am
2pm
Time
6pm
10pm
Available Data
• Forecasted Load
– Hourly demand for one year
• Forecasted Market Prices
• Fixed Contract prices
Model features
• Flexible: Let the user input values for all
parameters.
• Accurate: It follows the power demand
closely by dividing the month into 150
periods.
• Handle risk: Control exposure to spot
market for different demand loads.
• Automated
Subscripts
b=Block index (1,…,5)
d=Day index (1,…,31)
K=Week index (1,…,5)
Decision variables
• Power from WAPAbd
• MAX
• Power from High Load Forward
• Power from Low Load Forward
• Power from All Week Forward
• Power from E3bk
Parameters
• Upper and Lower limit for WAPA
• WAPA capacity cost
• Variable Cost of each product
• Demand Loadbd, during each period
Objective function
MIN
SSSCost of Product bdk * Product bdk
+ (WAPA Capacity Cost * MAX)
- SSS(Load bdk - Product bdk)*Cost Forward bdk
Constraints
• WAPA Upper and Lower limit constraints
• MAX >= WAPAbd.
• Satisfy all demand
• All variables >= 0.
Model: Inputs
INPUT PARAMETERS
Start Date
12/1/98
WESTERN
Capacity cost, $/KW-mo
Variable cost, $/MWH
Transmission cost
$/MWH
HIGH LOAD FORWARD
5
11.236
2
140000
61250
LOW LOAD FORWARD
ASK: Price, $/MWH
BID: Price, $/MWH
20
21
ALL WEEK FORWARD
ASK: Price, $/MWH
BID: Price, $/MWH
15
16
FORWARD TRANSMISSION COST
ASK: Price, $/MWH
BID: Price, $/MWH
18
19
E3 BLOCKS
Transaction cost
Block
(1) 6AM-10AM
(2) 10AM-2PM
(3) 2PM-6PM
(4) 6PM-10PM
Upper limit, Kwh
Lower limit,Kwh
0.03
1
18
20
24
22
Cost, $/MWH
Transmission Cost
$/MWH
Week (No transaction cost)
2
3
18
18
20
20
24
24
22
22
4
4
4
18
20
24
22
5
18
20
24
22
Quantifying Risk
• Risk Defined:
– exposure to spot market
• Risk Implementation
– % exposure to spot market
• during high load periods
• during normal load periods
Model: Quantifying
Risk
• Risk is the exposure to the spot market
Percentage of load EXPOSED to spot market
Definition
High Load
Block
1
2
3
4
5
140000
Time
10PM-6AM, Sun.
6AM-10AM
10AM-2PM
2PM-6PM
6PM-10PM
Percentage
High Load
Normal
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
DECISION VARIABLES
WESTERN
Model:
Outputs
for all productdecision variables
Block 1
Block 2
Block 3
Block 4
Block 5
12/1/98
112284.5
112284.5
112284.5
112284.5
112284.5
Maximum
112284.5
12/2/98
112284.5
112284.5
112284.5
112284.5
112284.5
HIGH LOAD FORWARD (6 a.m. to 10 p.m.)
Allocation to High Load
Forward
56346.75
LOW LOAD FORWARD (10 p.m. to 6 p.m.)
Allocation to Low Load
Forward
14178.5
ALL WEEK FORWARD (24 hours a day, 7 days a week)
Allocation to All Week
Forward
0
E3 BLOCKS
Block
6AM-10AM
10AM-2PM
2PM-6PM
6PM-10PM
Week 1
0
0
0
0
Total
Cost
$
$
$
$
$
-
12/3/98
112284.5
112284.5
112284.5
112284.5
112284.5
12/4/98
112284.5
112284.5
112284.5
112284.5
112284.5
Minimized
Objective
Function
12/5/98
112284.5
112284.5
112284.5
112284.5
112284.5
Total Cost Western
the costs for
different products
12/7/98
108148.625
112284.5
112284.5
112284.5
112284.5
$ 1,614,778.87
Capacity Cost $ 561,422.50
$1,809,351.92
Model
Outputs:
12/6/98
112284.5
112284.5
112284.5
112284.5
112284.5
Total Cost High Load Forward
$
608,544.90
Total Cost Low Load Forward
$
88,473.84
Total Cost All Week Forward
$
Week 2
0
0
0
0
Total
Cost
$
$
$
$
$
Total Cost E3 Blocks
-
Week 3
-
0
0
0
0
Total
$
-
The Option to Sell Back
LOAD - POWER BOUGHT
Negative means
unused capacity
Unused capacity
multiplied by the
corresponding
price
Day
Block
Block
Block
Block
Block
1
2
3
4
5
1
-13139.25
-39857
-7472
-12084.25
-12680.25
2
-11321.125
-37829.5
-2043.75
0
-48.75
3
-8175
-37147.5
-8426
-8733
-3434.75
12/02/98
1720811
3328996
196200
0
5070
12/03/98
1242600
3268980
808896
978096
357214
Expected Revenue
Date
Block
Block
Block
Block
Block
1
2
3
4
5
12/01/98
1997166
3507416
717312
1353436
1318746
Sum Of The Expected Revenue
$ 502,445.68
Revenue from
selling back
Chart Output:
Percentage of
different products
The portfolio of electricity procurement for Dec
1998
100%
Sell back to
Market
60%
E3 blocks
40%
LL Forward
20%
HL
Forward
0%
-20%
WAPA
date
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
-40%
1
percentage of different products
80%
Quantifying
Results
Model Comparison
• Run models under various scenarios
– Heavy load
– Light load
– Normal load
• Calculate cost reduction under new
model
Model Comparison
• Based on same inputs
– prices
– forecasted demand
• Compare models against an actual
load
– Actual load = average load during time
intervals utilized in UCB model
Model Comparison
• UCB Model is inherently better than
Palo Alto’s current Model.
L
o
a
d
6am
10am
2pm
Time
6pm
10pm
Monthly
Savings
1998 Electricity Costs
2500000
2000000
1500000
$
1000000
500000
0
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Nov Dec
Month
Annual Savings
1998 Annual Cost
Palo Alto Model
UCB Model
$26,200,000.00
UCB Model with
Revenue
$26,000,000.00
$25,800,000.00
$25,600,000.00
$25,400,000.00
$25,200,000.00
$25,000,000.00
$24,800,000.00
$24,600,000.00
$24,400,000.00
$24,200,000.00
$24,000,000.00
1998
Reduction in
Variance
Comparison of Variance (March)
600,000,000.00
500,000,000.00
400,000,000.00
300,000,000.00
10pm-6am
200,000,000.00
6pm-10pm
2pm-6pm
100,000,000.00
10am-2pm
-
6am-10am
Palo Alto
UCB
Summary of
Results
• UCB Model Savings
– $1.121 million for 1998
– 4% cost reduction
• UCB with revenue Model
– additional $180,762 for 1998
– additional 1% cost reduction
• Reduction in Variance
Benefits of UCB
Model
• Utilizes all available procurement
options
• Low Run-time
• Partitions day into finer time intervals
– more closely follows demand curve
– reduction in variance from actual load
• Reduction in risk
Recommendations
• Replace existing model with UCB
model
• Negotiate with WAPA to reduce
lower capacity limit
– For June 1998, the max purchase
quantity is ~ 40 mwh (no lower
capacity limit)
• Incorporate spot market into
decisions